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Putnam
2014 Putnam
5
Putnam 2014 A5
Putnam 2014 A5
Source:
December 7, 2014
Putnam
algebra
polynomial
MIT
inequalities
Putnam 2014
Problem Statement
Let
P
n
(
x
)
=
1
+
2
x
+
3
x
2
+
⋯
+
n
x
n
−
1
.
P_n(x)=1+2x+3x^2+\cdots+nx^{n-1}.
P
n
(
x
)
=
1
+
2
x
+
3
x
2
+
⋯
+
n
x
n
−
1
.
Prove that the polynomials
P
j
(
x
)
P_j(x)
P
j
(
x
)
and
P
k
(
x
)
P_k(x)
P
k
(
x
)
are relatively prime for all positive integers
j
j
j
and
k
k
k
with
j
≠
k
.
j\ne k.
j
=
k
.
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